An incremental algorithm for updating betweenness centrality and k-betweenness centrality and its performance on realistic dynamic social network data

  • Miray Kas
  • Kathleen M. Carley
  • L. Richard Carley
Original Article


The increasing availability of dynamically changing digital data that can be used for extracting social networks over time has led to an upsurge of interest in the analysis of dynamic social networks. One key aspect of dynamic social network analysis is finding the central nodes in a network. However, dynamic calculation of centrality values for rapidly changing networks can be computationally expensive, with the result that data are frequently aggregated over many time periods and only intermittently analyzed for centrality measures. This paper presents an incremental betweenness centrality algorithm that efficiently updates betweenness centralities or k-betweenness centralities of nodes in dynamic social networks by avoiding re-computations through the efficient storage of information from earlier computations. In this paper, we evaluate the performance of the proposed algorithms for incremental betweenness centrality and k-betweenness centrality on both synthetic social network data sets and on several real-world social network data sets. The presented incremental algorithm can achieve substantial performance speedup (3–4 orders of magnitude faster for some data sets) when compared to the state of the art. And, incremental k-betweenness centrality, which is a good predictor of betweenness centrality, can be carried out on social network data sets with millions of nodes.


Betweenness centrality k-Betweenness centrality Incremental algorithms Dynamic network analysis All-pairs shortest paths 



This work is supported in part by the Defense Threat Reduction Agency (HDTRA11010102), and by the center for Computational Analysis of Social and Organizational Systems (CASOS) at Carnegie Mellon. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied by the DTRA or the US government. This work is done when Miray Kas was a Ph.D. student in Carnegie Mellon University’s Electrical and Computer Engineering department.


  1. Bader D, Madduri K (2006) Parallel algorithms for evaluating centrality indices in real-world networks. International conference on parallel processing (ICPP). IEEE, pp 539–550Google Scholar
  2. Barabasi A, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512CrossRefMathSciNetGoogle Scholar
  3. Batagelj V, Kejžar N, Korenjak-Černe S, Zaveršnik M (2006). Analyzing the structure of US patents network. Springer, BerlinGoogle Scholar
  4. Berman AM (1992) Lower and upper bounds for incremental algorithms. Ph.D. Dissertation, The State University of New Jersey at Rutgers, Computer Science, New BrunswickGoogle Scholar
  5. Borgatti SP, Everett MG (2006) A graph-theoretic perspective on centrality. Soc Netw 28(4):466–484CrossRefGoogle Scholar
  6. Brandes U (2001) A faster algorithm for betweenness centrality. J Math Sociol 25(2):163–177CrossRefzbMATHGoogle Scholar
  7. Brandes U (2008) On variants of shortest-path betweenness centrality and their generic computation. Soc Netw 30(2):136–145CrossRefMathSciNetGoogle Scholar
  8. Demetrescu C, Italiano GF (2004) A new approach to dynamic all pairs shortest paths. J ACM (JACM) 51(6):968–992CrossRefMathSciNetzbMATHGoogle Scholar
  9. Demetrescu C, Italiano GF (2006) Experimental analysis of dynamic all pairs shortest path algorithms. ACM Trans Algorithms (TALG) 2(4):578–601CrossRefMathSciNetGoogle Scholar
  10. Dijkstra E (1959) A note on two problems in connexion with graphs. Numer Math 1(1):269–271CrossRefMathSciNetzbMATHGoogle Scholar
  11. Even S, Gazit H (1985) Updating distances in dynamic graphs. Methods Oper Res 49:371–387MathSciNetzbMATHGoogle Scholar
  12. Floyd R (1962) Algorithm 97: shortest path. Commun ACM 5(6):345CrossRefGoogle Scholar
  13. Fredman ML, Tarjan RE (1984). Fibonacci heaps and their uses in improved network optimization algorithms. 25th annual symposium on foundations of computer science. IEEE, pp 338–346Google Scholar
  14. Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40(1):35–41CrossRefGoogle Scholar
  15. GraphStream Team (2010) GraphStream. Retrieved 3 February 2012.
  16. Green O, McColl R, Bader DA (2012). A fast algorithm for streaming betweenness centrality. International Conference on Privacy, Security, Risk and Trust (PASSAT) and International Conference on Social Computing (SocialCom). IEEE, Amsterdam, pp 11–20Google Scholar
  17. Gringoli FE (2009) GT: picking up the truth from the ground for internet traffic. Comput Commun Rev 39(5):13–18CrossRefGoogle Scholar
  18. Habiba H, Tantipathananandh C, Berger-Wolf T (2007) Betweenness centrality measure in dynamic networks. University of Illinois at Chicago, Department of Computer Science. DIMACS, ChicagoGoogle Scholar
  19. Isella LE (2011) What’s in a crowd? Analysis of face-to-face behavioral networks. J Theor Biol 271(1):166–180CrossRefMathSciNetGoogle Scholar
  20. Jiang K, Ediger D, Bader DA (2009) Generalizing k-betweenness centrality using short paths and a parallel multithreaded implementation. International conference on parallel processing (ICPP), Vienna, pp 542–549Google Scholar
  21. Kas M (2013b) Incremental centrality algorithms for dynamic network analysis. Ph.D. Dissertation, Carnegie Mellon University, ECE, PittsburghGoogle Scholar
  22. Kas M, Wachs M, Carley L, Carley K (2012a). Incremental centrality computations for dynamic social networks. XXXII international sunbelt social network conference (Sunbelt 2012). INSNA, Redondo BeachGoogle Scholar
  23. Kas M, Carley KM, Carley LR (2012b) Trends in science networks: understanding structures and statistics of scientific networks. Social network analysis and mining (SNAM)Google Scholar
  24. Kas M, Wachs M, Carley K, Carley L (2013) incremental algorithm for updating betweenness centrality in dynamically growing networks. The 2013 IEEE/ACM international conference on advances in social networks analysis and mining (ASONAM). IEEE, Niagara FallsGoogle Scholar
  25. Kim H, Anderson R (2012) Temporal node centrality in complex networks. Phys Rev E 85(026107):1–8zbMATHGoogle Scholar
  26. King, V. (1999). Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. 40th annual symposium on foundations of computer science. IEEE, pp 81–89Google Scholar
  27. Kourtellis N, Alahakoon T, Simha R, Iamnitchi A, Tripathi R (2013) Identifying high betweenness centrality nodes in large social networks. Soc Netw Anal Min (SNAM) 4(3):899–914CrossRefGoogle Scholar
  28. Lee MJ, Lee J, Park JY, Choi R, Chung CW (2012a) QUBE: a Quick algorithm for updating BEtweenness centrality. WWW, ACM, pp 351–360Google Scholar
  29. Lee MJ, Lee J, Park JY, Choi R, Chung CW (2012b) QUBE: a quick algorithm for updating BEtweenness centrality. In: Proceedings of the 21st international conference on World Wide Web (WWW). ACM, Lyon, pp 351–360Google Scholar
  30. Lerman K, Ghosh R, Kang JH (2010) Centrality metric for dynamic networks. 8th workshop on mining and learning with graphs (MLG). ACM, pp 70–77Google Scholar
  31. Leskovec J, Kleinberg J, Faloutsos C (2007) Graph evolution: densification and shrinking diameters. ACM Trans KDD 1(2):1–41Google Scholar
  32. Leskovec J, Huttenlocher DP, Kleinberg JM (2010) Governance in social media: a case study of the Wikipedia promotion process. The international AAAI conference on weblogs and social media (ICWSM)Google Scholar
  33. Liao W, Ding J, Marinazzo D, Xu Q, Wang Z, Yuan C et al (2011) Small-world directed networks in the human brain: multivariate Granger causality analysis of resting-state fMRI. Neuroimage 54(4):2683–2694CrossRefGoogle Scholar
  34. Norlen K, Lucas G, Gebbie M, Chuang J (2002) EVA: extraction, visualization and analysis of the telecommunications and media ownership network. International telecommunications society 14th biennial conferenceGoogle Scholar
  35. Onnela JP, Saramäki J, Hyvönen J, Szabó G, Lazer D, Kaski K et al (2007) Structure and tie strengths in mobile communication networks. Proc Natl Acad Sci 104(18):7332–7336CrossRefGoogle Scholar
  36. Opsahl T, Panzarasa P (2009) Clustering in weighted networks. Soc Netw 31(2):155–163CrossRefGoogle Scholar
  37. Pfeffer J, Carley KM (2012) k-Centralities: local approximations of global measures based on shortest paths. WWW. ACM, pp 1043–1050Google Scholar
  38. Puzis R, Zilberman P, Elovici Y, Dolev S, Brandes U (2012) Heuristics for speeding up betweenness centrality computation. Social computing and on privacy, security, risk and trust. IEEE Computer Society, pp 302–311Google Scholar
  39. Ramalingam G, Reps T (1991a) On the computational complexity of incremental algorithms. Technical report, University of Wisconsin at MadisonGoogle Scholar
  40. Ramalingam G, Reps T (1991b) On the computational complexity of incremental algorithms. Technical Report, University of Wisconsin at Madison, Computer Science, MadisonGoogle Scholar
  41. Ramezanpour A, Karimipour V (2008) Simple models of small world networks with directed links. Sharif University of Technology, Department of Physics, TehranGoogle Scholar
  42. Renyi A, Erdos P (1959). On random graphs. Publicationes Mathematicae, 6Google Scholar
  43. Tang J, Musolesi M, Mascolo C, Latora V, Nicosia V (2010) Analysing information flows and key mediators through temporal centrality metrics. 3rd workshop on social network systems (SNS). AprilGoogle Scholar
  44. Watts D, Strogatz S (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442Google Scholar
  45. Xu J (2008) Markov chain small world model with asymmetric transition probabilities. Electron J Linear Algebra 17:616–636MathSciNetzbMATHGoogle Scholar
  46. Yang J, Leskovec J (2011). Patterns of temporal variation in online media. International conference on web search and data minig (WSDM). ACMGoogle Scholar
  47. Zhu C, Xiong S, Tian Y, Li N, Jiang K (2004). Scaling of directed dynamical small-world networks with random responses. Phys Rev Lett 92 218702(24):1–4Google Scholar

Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  • Miray Kas
    • 1
    • 2
  • Kathleen M. Carley
    • 2
  • L. Richard Carley
    • 2
  1. 1.Google Inc.Menlo ParkUSA
  2. 2.Center for Computational Analysis of Social and Organizational Systems (CASOS)Carnegie Mellon UniversityPittsburghUSA

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